Problem: Let $h(x)=-5\cdot6^x$. Find $h'(x)$. Choose 1 answer: Choose 1 answer: (Choice A) A $-5\cdot 6^x\ln(x)$ (Choice B) B $-5\cdot 6^{x}$ (Choice C) C $-5\cdot 6^{x-1}$ (Choice D) D $-5\cdot 6^x\ln(6)$
Solution: The expression for $h(x)$ includes an exponential term. Remember that the derivative of the general exponential term $a^x$ (where $a$ is any positive constant) is $\ln(a)\cdot a^x$. Put another way, $\dfrac{d}{dx}(a^x)=\ln(a)\cdot a^x$. $\begin{aligned} h'(x)&=\dfrac{d}{dx}(-5\cdot6^x) \\\\ &=-5\dfrac{d}{dx}(6^x) \\\\ &=-5\cdot\ln(6)\cdot6^x \\\\ &=-5\cdot 6^x\ln(6) \end{aligned}$ In conclusion, $h'(x)=-5\cdot 6^x\ln(6)$.